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Table 1.7
Intuitionistic
fuzzy decision matrix
R
(
3
)
y
1
y
2
y
3
y
4
G
1
(0.5,0.4,0.1)
(0.6,0.4,0.0)
(0.3,0.7,0.0)
(0.2,0.7,0.1)
G
2
(0.5,0.4,0.1)
(0.7,0.3,0.0)
(0.6,0.4,0.0)
(0.5,0.3,0.2)
G
3
(0.6,0.2,0.2)
(0.3,0.5,0.2)
(0.3,0.5,0.2)
(0.9,0.1,0.0)
G
4
(0.3,0.5,0.2)
(0.5,0.5,0.0)
(0.6,0.2,0.2)
(0.6,0.4,0.0)
⎛
⎞
.
.
.
.
0
3909 0
3937 0
3909 0
3847
⎝
⎠
0
.
3892 0
.
3892 0
.
3921 0
.
3892
1
=
0
.
3811 0
.
3864 0
.
3829 0
.
4000
0
.
3864 0
.
3829 0
.
3909 0
.
3921
⎛
⎞
0
.
3046 0
.
2992 0
.
3046 0
.
3115
⎝
⎠
0
.
3015 0
.
3015 0
.
2960 0
.
3015
2
=
0
.
3055 0
.
3068 0
.
3085 0
.
3124
0
.
3068 0
.
3085 0
.
3046 0
.
3119
⎛
⎞
0
.
3046 0
.
3070 0
.
3046 0
.
3038
⎝
⎠
0
.
3093 0
.
3093 0
.
3119 0
.
3093
3
=
0
.
3134 0
.
3068 0
.
3085 0
.
2876
0
.
3068 0
.
3085 0
.
3046 0
.
2960
Step 2
Utilize the IFPWA operator (
1.26
) to aggregate all the individual intu-
itionistic fuzzy decision matrices
R
(
k
)
=
(
r
(
k
)
ij
)
4
×
4
(
=
,
,
)
k
1
2
3
into the collective
=
(
r
ij
)
4
×
4
:
intuitionistic fuzzy decision matrix
R
⎛
⎝
(
0
.
4052
,
0
.
4938
,
0
.
1010
)(
0
.
5069
,
0
.
3670
,
0
.
1261
)(
0
.
2038
,
0
.
7962
,
0
.
0000
)
(
0
.
4466
,
0
.
4667
,
0
.
0867
)(
0
.
6086
,
0
.
3355
,
0
.
0559
)(
0
.
6183
,
0
.
2910
,
0
.
0907
)
R
=
(
0
.
6162
,
0
.
2334
,
0
.
1504
)(
0
.
2321
,
0
.
5288
,
0
.
2391
)(
0
.
3707
,
0
.
5005
,
0
.
1288
)
(
0
.
3323
,
0
.
5365
,
0
.
1312
)(
0
.
5332
,
0
.
3838
,
0
.
0830
)(
0
.
5062
,
0
.
2263
,
0
.
2675
)
⎞
⎠
(
0
.
2401
,
0
.
5862
,
0
.
1737
)
(
0
.
6070
,
0
.
2562
,
0
.
1368
)
(
0
.
6668
,
0
.
1242
,
0
.
2090
)
(
.
,
.
,
.
)
0
7214
0
1507
0
1279
in the
j
th column
of
R
by using the IFWA operator (
1.57
), and get the overall preference value
r
j
corresponding to the alternative
y
j
:
Step 3
Aggregate all the preference values
r
ij
(
j
=
1
,
2
,
3
,
4
)
r
1
=
(
0
.
4642
,
0
.
4105
,
0
.
1253
),
r
2
=
(
0
.
4857
,
0
.
3967
,
0
.
1176
)
r
3
=
(
0
.
4322
,
0
.
4286
,
0
.
1392
),
r
4
=
(
0
.
5710
,
0
.
2464
,
0
.
1826
)
Step 4
By Eq. (
1.3
), we calculate the scores of
r
j
(
j
=
1
,
2
,
3
,
4
)
respectively:
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